Kinetic Studies of the Flagellar Movement of Sea-Urchin Spermatozoa

In previous papers (Holwill & Silvester, 1965, 1967) results have been presented which support the hypothesis that the frequency of beating of a flagellum (hereinafter referred to simply as ‘frequency’ ) is identical with, or at least proportional to, a rate constant of the first-order chemical reaction which limits the frequency. If, as seems probable (e.g. Bishop, 1962; Brokaw, 1962) adenosine triphosphate (ATP) is directly involved in the supply of energy to an active organelle, then the experimental evidence indicates that the rate-limiting reaction is the breakdown of an ATP-ATPase complex.

It has been found possible to treat certain flagella with solutions containing glycerol in such a way that these appendages can be reactivated by the addition of ATP, the frequency being controlled by the ATP concentration (e.g. Hoffmann-Berling, 1955 ; Brokaw, 1961, 1967). Earlier workers (e.g. Bishop, 1958; Bishop & Hoffmann-Berling, 1959) reported that the re-activated appendages exhibited only local oscillations but more recently Brokaw (1962, 1963) and Gibbons (1965c) have prepared ‘models’ in which all the features of normal wave propagation are preserved. The relation between frequency and ATP concentration is found to be similar in form to the Michaelis-Menten law of enzyme kinetics (Brokaw, 1967; Brokaw & Holwill, 1967). The glycerinated models appear to provide an externally controllable system in which all the machinery for wave propagation is preserved and are potentially suitable for further studies of the thermodynamic aspects of flagellar movement. In this paper the reactions of sea-urchin spermatozoa are investigated in an attempt to characterize further the enzymatic reactions which underly flagellar motility.

This treatment follows closely Lineweaver & Burke’ s (1934) analysis of the Michaelis-Menten equation.

Laidler (1955 a, b) has developed an extensive theory pertaining to the effects of pH change on the rates of enzyme reactions. If the rate of the enzyme reaction passes through a maximum as the pH is varied, it is necessary to assume that the enzyme contains an acidic and a basic group, both of which take part in the reaction. It is possible that one, both or neither of these groups is involved in complex formation, but if the reaction passes through a maximum both groups must be involved in the breakdown of the complex. Laidler derives equations relating the reaction rate to the hydrogen-ion concentration for each of the four possible ways in which the activated complex may be formed. In each case, on the acidic side of the optimum pH he predicts that a graph of V_max/V (V_max and V are the velocities of the reaction at the optimum pH and the given pH respectively) against the hydrogen-ion concentration [H+] should be linear. On the basic side of the optimum pH, it is predicted that in all cases except where complex formation involves the basic group of the enzyme only, a plot of V_max/V against 1/[H⁺] should be linear; for the exception a linear variation of V_max/V with [H⁺] is predicted.

The slopes of the graphs are related to equilibrium constants for reactions involving the enzyme, enzyme-substrate complex and the hydrogen ions. The way in which the constant K varies with pH change is also dependent on the type of complexing involved in the reaction, as is the position of the pH optimum at different substrate concentrations.

More complex treatments involving the interaction of dipoles also predict a linear dependence of In A on 1/ε but in this case the slope of the graph involves the dipole moments of both reactants and of the resulting complex. Further analysis of the effect of the dielectric constant on reaction rates is undertaken in the discussion.

Spermatozoa from the sea-urchins Lytechmus pictus and Strongylocentrotus pur-puratus were obtained and prepared using the methods described by Brokaw (1965, 1966, 1967). Frequency determinations were made stroboscopically, the organisms being viewed under conditions of dark-field illumination.

The temperature of the preparation was varied by passing heated or cooled water (containing a small percentage of ethylene glycol to prevent freezing at low temperatures) through the specially modified microscope stage. Measurement of the temperature of the preparation was achieved by using a thermocouple inserted in a hole bored through the centre of a microscope slide; a potentiometer arrangement allowed a null-point detection method to be used and suitable resistances were chosen to permit the temperature to be read directly from the dial of a helical potentiometer (Holwill & Silvester, 1967). The calibration technique employed (Holwill & Silvester, 1967), introduces a maximum error of 0·3° C. in temperature over the range used. The scale could be read to within ± 0·1°C.

Variations in the dielectric constant of the medium were made by adding small amounts of methanol to the re-activation solution, while the ionic strength was altered by changing the potassium chloride concentration.

The frequencies of both intact and re-activated glycerinated spermatozoa were measured at a variety of temperatures between 5 and 30° C. For the glycerinated spermatozoa observations were made over a range of ATP concentrations from 10⁻⁴ to 10⁻³ M. For each frequency determination 20 spermatozoa were selected at random and an average frequency was obtained ; at a given temperature the frequency of the population was constant to within 10% of the average value. Since the frequency is known to change with altering viscosity all frequencies were corrected for the viscosity change which occurs with changing temperature using the results of Brokaw (1966) and M. E. J. Holwill (unpublished results). The corrected frequencies are those expected in a medium of viscosity 1 centipoise.

Figure 1 is a plot of ln f/T against 1/T for intact Lytechinus spermatozoa. The curve is linear over the range 5–21° C., but above 21° C. there is no correlation between the two parameters. A similar curve was obtained for Strongylocentrotus spermatozoa.

From the slope and intercept of the calculate regression line of the straight region of each curve average values for ΔH^‡ and ΔS^‡ were obtained (Table 1). At temperatures above 21° C. the preparations appeared to deteriorate rapidly and afforded no opportunity to investigate the movement on lowering the temperature.

The straight line of Fig. 2 is the regression line of ΔH^‡ upon ΔS^‡ previously derived from observations on large numbers of cilia and flagella (Holwill & Silvester, 1967). The points derived for sea-urchin spermatozoa are also plotted in Fig. 2 and, within the limits of experimental error, lie on the regression line.

The variation of the reciprocal of frequency with the reciprocal of the ATP concentration for glycerinated models of Lytechinus spermatozoa at different temperatures is shown in Fig. 3. (Similar results were obtained for Strongylocentrotus spermatozoa.) At each temperature a linear relationship was obtained, showing that equation (5) holds. From the regression lines values of f_max and (equation (5)) were obtained at each temperature.

In Fig. 4 are plotted the variations with 1/T of ln f_max/T and of In f/T at various ATP concentrations for spermatozoa of Lytechinus. (Graphs of similar character were obtained for Strongylocentrotus spermatozoa.) The curves for f_max and low ATP concentrations (3 × 10⁻⁴ M) are linear, and allow the calculation of activation entropies and enthalpies (see Table 1) while the graph at a 1 mM concentration shows some curvature. A graph of In against 1/T for spermatozoa of Lytechinus is shown in Fig. 5. This curve, and the corresponding one for Strongylocentrotus spermatozoa, are both approximately linear over the range of temperatures in which studies were made, thus permitting the calculation of activation parameters (see Table 1) whose significance will be discussed later. For comparison with other results all the thermodynamic data calculated here are plotted on Fig. 2.

Glycerinated spermatozoa from Strongylocentrotus were examined over a wide range of pH values at high (10⁻³ M) and low (10⁻⁴ M) ATP concentrations. The results are presented in Fig. 6 in which frequency is plotted against pH. At each concentration of ATP there is an optimum pH range centred at about pH 8·0. In the range pH 7·0–9·0 all motile organisms maintained progressive waves on their flagella. The number of motile organisms was about 40–50 % of the total population, as is normally seen in preparations of this nature. In the regions below pH 7–0 and above pH 9–0 the number of moving spermatozoa fell rapidly to about 5 % of the total population and the movements observed were mainly localized oscillations.

Frequency measurements were also made on Strongylocentrotus spermatozoa at several ATP concentrations while the pH was maintained at 7·5, 8·0 and 8·5. At each pH graphs were drawn of the reciprocal of the frequency against the reciprocal of the ATP concentration (Fig. 7). The two results obtained in the previous study at both pH 7·0 and pH 9·0 are also plotted on this graph. Values of (from the slope) and f_max from the intercept are given in Table 2. Although the values for f_max show some variation, the values of are equal within the limits of experimental error, except at the high and the low pH values.

Figure 8 shows the variation of f´/f with [H⁺] on the acidic side of the pH optimum (f′ is the value of the frequency at the optimum pH) while Fig. 9 is a plot of f′/ f against 1/[H⁺] on the basic side of the pH optimum. Linear relationships are obtained in all cases, but whereas the slopes of the lines at the two ATP concentrations in Fig. 9 are roughly equal, in Fig. 8 they are certainly different.

The variation of frequency with pH was also examined for glycerinated Lytechinus spermatozoa at an ATP concentration of 10⁻³ M. The relationship is qualitatively similar to that for Strongylocentrotus spermatozoa, but the optimum value of the pH is about 8·5. Abnormalities were again noticed in the movements of spermatozoa outside the range pH 7·0–9·0. Linear relationships were obtained between f′/f and [H⁺] on the acidic side of the optimum pH and between f′/f and 1 /[H⁺] on the basic side, although some deviation occurs near the optimum pH in the latter case.

Suspensions of glycerinated spermatozoa from Strongylocentrotus were subjected to varying concentrations of methanol in an attempt to discover the effects of changing the dielectric constant of the medium on the frequency. The ATP concentration was maintained at 10⁻³ M. Figure 10 is a graph of the logarithm of the frequency against the reciprocal of the dielectric constant (ε). For/e in the range 1·23 × 10⁻² to 1·28 × 10⁻² the graph is linear with a slope of − I·88 ± O·2 × 10³. Further examination of these results will be deferred to the discussion.

Figure 11 depicts the variation of the frequency of glycerinated spermatozoa from Strongylocentrotus with the ionic strength (u) of the medium. It can be seen that the frequency passes through a maximum in the region u = 0·5. At low ( < 0·1) and high ( > 0·5) ionic strengths the number of motile organisms was much less than normal, and the movements observed were erratic and irregular, often consisting of localized oscillations. Figure 12 shows a graph of log₁₀f against √u for the region of ionic strength in which normal movement was observed. The graph is curved, in contrast to the prediction of equation (11) and the results of Hoffmann-Berling for locust spermatozoa.

The results summarized by Fig. 1 confirm an earlier subjective impression (Holwill & Silvester, 1967) that at the higher temperatures the frequencies are lower than those required to give a consistent linear relationship between f/T and 1/T. The behaviour shown in Fig. 1 is typical of the temperature dependence of the rate of enzyme reactions, the curvature being attributed to denaturation of the enzyme. For the spermatozoa of Lytechinus and Strongylocentrotus and for the spermatozoa from several marine organisms (M. E. J. Holwill, unpublished results) the curvature (and presumably the denaturation of the enzyme which participates in the reaction providing energy for the motile process) occurs at a lower temperature than for other organisms (Holwill & Silvester, 1967). This observation could result from one of two situations. In the first, the enzymes differ slightly in structure from one organism to another so that the number or type of bonds which need to be broken for denaturation to occur is variable among organisms ; consequently the denaturation energy (and hence effect of temperature) could change from one species to another. In the second, the enzymes are identical in all organisms but the environmental conditions (e.g. pH, ionic strength, etc.) are variable and are such as to favour denaturation at lower temperatures in the spermatozoa of marine organisms than in others. The effect could be associated with the fact that marine organisms normally encounter lower environmental temperatures (in the region of 16° C.) than many of the organisms previously examined by Holwill & Silvester (1967). For example, mammalian spermatozoa and ciliated lung tissue are normally exposed to temperatures of the order of 37° C.

The results obtained from the variation of frequency with temperature for both live and glycerinated sea-urchin spermatozoa conform to the linear pattern of activation parameters obtained earlier for a number of flagellates and ciliates (see Fig. 2 and Holwill & Silvester (1967)), thereby suggesting that the chemical reaction which limits the frequency of the sperm tails is similar to that in other flagellates. It may be significant that for the two species of sea-urchin the thermodynamic parameters characteristic of the rate-limiting step in the live spermatozoa are the same as those in the glycerinated models within the limits of experimental error. This observation strongly suggests that the reactions in vitro are identical with those in vivo, but further work on a variety of glycerinated flagellates is needed to test this conclusion.

Since the relation between frequency and ATP concentration appears to follow Briggs-Haldane kinetics, the variation of f_max with temperature essentially represents the variation of k₂ with temperature, since the total enzyme concentration is constant (see equation (4)). Since k₂ is the rate constant applicable to the breakdown of an enzyme-substrate complex the activation parameters derived from a plot of In k2/T against 1/T are those corresponding to this breakdown. It is necessary to examine the constants derived from the/_max plots to see how they are related to those of complex breakdown. Since AH* is determined by the slope of the graph, its value is independent of the magnitude of the constant [E0]/α (equation (4)), whereas this is not true for ΔS^‡, which is obtained from the intercept of the line ; it is thus possible that the entropies derived are not those of the chemical reaction which limits the frequency but contain an additional term that is constant for all organisms. If each enzyme molecule is used once per beat (the available experimental evidence does not contradict this (Brokaw, 1967)), then the constant E₀/α is unity. In any event the linearity of the AS* against ΔH^‡ plot indicates that the constant E₀/α. is the same for all flagella so far examined, and is of such a value as to allow the point corresponding to the breakdown of an ATP-myosin complex to fall close to the line. The close correspondence of the entropies and enthalpies obtained from the live spermatozoa and the f_max of glycerinated spermatozoa supports the earlier conclusion (Holwill & Silvester, 1967) that the rate-limiting step within a flagellum is the breakdown of an ATP-ATPase complex.

The activation parameters derived for glycerinated spermatozoa may be discussed in terms of the enzymic reaction (equation (1)) used to derive the Briggs-Haldane equation (equation (2)). It must be pointed out, however, that equation (1) may not be truly representative of the chemical reactions occurring within the flagellum; for example, there might be intermediate processes which would necessitate the introduction of further rate constants. The presence of such intermediate reactions would not necessarily alter the form of the Briggs-Haldane equation, but would certainly alter the significance of the constant and possibly also k₂ (see, for example, Laidler (1958)).

On the basis of simple Briggs-Haldane kinetics, k₋₁ should be larger than k₂ to be consistent with the results, leading to the conclusion that the limiting chemical reaction in flagella is the breakdown of an enzyme-substrate complex.

The general nature of the effects on the frequency of changing the hydrogen-ion concentration is similar to the variation in ATPase activity of glycerinated flagella subjected to similar treatment (e.g. Tibbs, 1957, 1959) in that the activity in both cases passes through a maximum. However, as pointed out by Gibbons (1966), no direct comparison can be made with the earlier results since the enzymic activity of glycerinated flagella is probably due to a mixture of ATPase components, whereas the frequency presumably derives from a single component (but see later). It is of greater interest to compare the frequency results with those obtained for dynein (Gibbons, 1966), the ATPase protein which has been isolated from Tetrahymena cilia and which is believed to play an important role in flagellar movement. Dynein is found in two forms (Gibbons, 1965a, b; Gibbons & Rowe, 1965), one sedimenting at 14S and the other at 30 S in the ultracentrifuge. The enzymic and physico-chemical properties of the two forms of dynein are consistent with the idea that the 30 S protein is a polymer of the 14S form (Gibbons, 1966; Gibbons & Rowe, 1965).

The ATPase activity of 30 S dynein varies little in the range of pH from 6-o to 9-0, whereas for 14 S dynein an optimum pH occurs, with a fairly broad maximum, in the region of pH 9-0 (Fig. 14). The different behaviour of the two types of dynein is attributed to the more unstable nature of 14S dynein under acid conditions.

The variations of frequency with pH for glycerinated spermatozoa at high concentrations of ATP (Fig. 6) are much closer to the curve for 14 S dynein than to that for 30 S dynein, although graphs similar to the observed frequency variations could be obtained by combining the two dynein curves in suitable proportions.

Caution must, of course, be exercised in the interpretation of the frequency results in terms of the activity of dynein in vivo since : (a) the dynein employed by Gibbons was obtained from Tetrahymena cilia while the observations of frequency were made on sea-urchin spermatozoa; (b) the results for dynein were obtained from experiments on extracted protein, whereas the frequency results derive from a physiologically intact mechano-chemical system ; and (c) Gibbons did not use KCl or urea in his assay solutions, whereas these compounds were both present in the solutions used here to re-activate the glycerinated flagella.

Although these facts must be borne in mind, the results lead one to speculate that dynein in the 14 S form is the more likely of the two types of protein to be involved in the motile process in vivo. Other work (Gibbons, 1965a, b) has shown, however, that 30 S dynein is the more physiologically active of the two types. Perhaps it is not unreasonable to suppose that, in the glycerinated organisms, both types of dynein contribute in some way to the bending of the flagellum and their combined ATPase activities manifest themselves in terms of the frequency. More confidence could be placed in this interpretation if it were shown that dynein extracted from sea-urchin spermatozoa had a variation of ATPase activity with pH similar to that of the dynein extracted from Tetrahymena cilia

It is, of course, possible, as suggested by C. J. Brokaw (personal communication), that the variations in frequency reflect the behaviour of an ATPase responsible for initiating the propagation of waves along the flagellum rather than that of an ATPase (dynein) distributed throughout the flagellum. If this is shown to be the case the preceding argument will be clearly invalid. The results of further experiments are necessary to test this idea.

Most of the results pertaining to the pH studies are consistent with the conditions derived by Laidler (1955b) for an enzyme in which both the acidic and basic groups of the enzyme participate in the reaction but where complexing with the substrate occurs at neither of these sites. Specifically, these conditions are: (a) the rate of reaction should pass through maxima at low and high substrate concentrations, (b) the pH optimum should be independent of the substrate concentrations, (c) the constant R should be independent of pH, and (d) on the acidic side of the pH optimum T_mai/F should be proportional to [H+], while on the basic side it should be proportional to 1/[H⁺], the proportionality constants in each case being independent of the substrate concentration.

For flagellar movement V = αf (equation (3)), so that the variation of f′/f essentially represents that of V_max/V. The investigations of the effect of pH changes on the movement of glycerinated sea-urchin spermatozoa are not comprehensive, but only one exception to the above conditions has so far been observed. This is in the plots for Strongylocentrotus spermatozoa of f′/f against [H⁺], on the acidic side of the pH optimum, where a difference occurs in the proportionality constants at low and high ATP concentrations. The discrepancy may be associated with the errors of measurement of the low frequencies found at low ATP concentrations, since considerable scatter was observed in the readings, particularly on the acid side of the pH optimum (Fig. 6).

The linear character of Figs. 8 and 9 supports the idea that the substrate does not change its state of ionization over the range of pH investigated (Laidler, 1955a, b).

This is in accord with a report by Phillips, George & Rutman (1966),who found that in the presence of excess magnesium the ionization constant of ATP is so altered that above pH 5·8 more than 80 % of the total ATP is in the form of Mg-ATP²⁻. Consequently, in the range of pH under discussion, the substrate will not sensibly change its state of ionization.

It is of interest to note that the values for K obtained here (∼2·5 × 10⁸ M⁻¹) are somewhat lower than that (∼ 10⁻⁶ M⁻¹) obtained for dynein but correspond closely to the value derived elsewhere for glycerinated spermatozoa of Lytechinus pictus (Brokaw, 1967). The difference between the two figures is evidently significant and may be associated with the different ionic conditions of the two systems.

When considering the results of variations in dielectric constant and ionic strength, the conclusion that the frequency is limited by the breakdown rather than the formation of an enzyme-substrate complex leads to a different inference from the one which was drawn in an earlier paper (Holwill & Silvester, 1965). In the earlier work examination of the results of Hoffmann-Berling (1955) relating to ionic strength led to the conclusion that the limiting reaction within the flagellum is one between ions of like sign. The arguments which lead to this deduction, however, are based on a model for complex formation and are derived from a consideration of the approach of two ions (see REACTION KINETICS, p. 205).

In the case where the dielectric constant is varied, equations will be obtained which are similar in character for either the breakdown of a complex or its formation. However, the electrostatic forces between ions are such that the conclusion to be drawn from a particular result will, in the case of breakdown, be directly opposite to that which would follow if one were considering complex formation.

The foregoing analysis presupposes that the only effect of the introduction of methanol into the medium is to change the dielectric constant of the flagellar environment. It is possible that other effects contribute to the change in frequency when various concentrations of methanol are introduced. Attempts to use other liquids, e.g. dioxane, as a substitute for the methanol resulted in the death of the organisms and it has not been possible to establish whether the only factor that changes in this case is the dielectric constant. These comments must be considered in relation to the foregoing analysis.

The results obtained from varying the ionic strength of the medium are more difficult to interpret in terms of complex breakdown since the simple Debye-Hückel theory, upon which equation (11) is based, fails when the concentration of ions becomes high. In the present case the 0·25 M concentration of KC1 is apparently too high for the simple theory to apply and probably accounts for the non-linearity of Fig. 12. If the more extensive Debye-Hückel theory is applied to the flagellar motion, equations are obtained that cannot be usefully interpreted in terms of the results obtained. The results are generally in agreement with those obtained by Hoffmann-Berling (1955), but it is apparent that a different interpretation is to be placed on these results from that discussed previously (Holwill & Silvester, 1965).

It is possible that the effects observed when the ionic strength was changed were due not only to the change in ionic strength produced by the addition of potassium chloride but also to the presence of the potassium chloride per se. Gibbons (1966) found that the activity of 30S dynein was enhanced when the KCl concentration was increased, while that of 14 S dynein was decreased. Again, as in the results from the pH studies, to obtain a curve from the dynein results that is similar in form to the frequency results (which pass through a maximum at an ionic strength of about 0·5 (Fig. 11) corresponding to a KCl concentration in the region of 0·2 M) it is necessary to assume that both 14S and 30S dynein participate in the process responsible for flagellar movement.

The fact that fairly extreme departures from the normal re-activation medium prepared for the flagellar models restricted the ability of an organelle to sustain a progressive wave suggests that these treatments (high or low pH, low ionic strength, high KC1 concentrations) in some way affect the mechanism responsible for wave propagation. Since the membrane is modified in some way by the procedures of glycerination, the ions introduced into the medium have access to all components of the flagellum, so that it is not possible to assign the function of propagation to any particular structure on the basis of the present results.

Evidence has been presented here that further supports the conclusion that the reaction which limits the frequency is the breakdown of an enzyme-substrate complex, and preliminary studies have been made to characterize more fully the enzymic reaction itself. These studies need to be extended in many ways, and it would be useful if studies could be made of the ATPase activity of dynein from the same organism that is used for frequency measurements.

I am grateful to Professor C. J. Brokaw for providing me with laboratory facilities at the California Institute of Technology where the experimental work described in this paper was carried out. I would like to thank Professor Brokaw and Dr N. R. Silvester for many valuable and stimulating discussions associated with the work described here.

The work was supported in part by U.S. Public Health Service Grant no. GM 14631.